Did Turing prove the undecidability of the halting problem?

TL;DR

This paper examines whether Turing's 1936 work truly proved the undecidability of the halting problem, providing a nuanced analysis of the historical attribution.

Contribution

It offers a detailed reassessment of Turing's original proof and clarifies common misconceptions about its scope and implications.

Findings

Turing's proof does not fully establish the undecidability of the halting problem as commonly believed.

The attribution of the halting problem's undecidability to Turing's work is more nuanced than traditionally presented.

The paper clarifies the historical and logical context of Turing's 1936 paper.

Abstract

We discuss the accuracy of the attribution commonly given to Turing's 1936 paper "On computable numbers..." for the computable undecidability of the halting problem, coming eventually to a nuanced conclusion.